It is shown that if the Cabibbo angle is introduced by an axial (and not vector) rotation
about the seventh axis in $SU_3$ -space, and it is assumed that the pion is massless before
the rotation, the well-known contradiction between the allowed regions of values of the
parameters of the broken $SU_3\otimes SU_3$ chiral symmetry can be eliminated. Different
models are discussed and an investigation made of the Hamiltonian of the $SU_3\otimes SU_3$ chiral symmetry breaking before the Cabibbo rotation. The results are generalized
to $SU_4\otimes SU_4$ . The invariance properties of the weak interactions under permutation of the quark isodoublets in the Glashow–Iliopoulos–Maiani model are used. Corresponding
unitary transformations are constructed and a theorem proved about the structure of the
Hamiltonian of the $SU_4\otimes SU_4$ chiral symmetry breaking.